J . A m . Chem. SOC. 1986, 108, 5793-5798
5793
Concerted Dihydrogen Exchange between Methanol and Formaldehyde. A Theoretical Study Michael L. McKee,*+ Philip B. Shevlin,*+and Henry S. Rzepa* Contribution from the Department of Chemistry, Auburn University, Auburn, Alabama 36849, and Department of Chemistry, Imperial College of Science and Technology, London, SW7 2AY, UK. Received February 18, 1986
Abstract: A detailed examination of the concerted dihydrogen transfer mechanism which transfers hydrogens f r o m methanol to formaldehyde h a s been carried o u t a t ab initio levels (3-21G, 6-31G*) a n d semiempirical levels ( M N D O , M N D O C ) . T h e transition structure h a s C2, symmetry a t the a b initio a n d MNDO levels, a n d t h e reaction h a s a 3 0 kcal/mol enthalpic barrier predicted a t the 6-31G* level including correlation effects and zero point correction. T h e MNDO method predicts thermodynamic properties a n d kinetic isotope effects ( K I E ) in good agreement with a b initio results. However, t h e M N D O enthalpic barrier disagrees with t h e a b initio barrier by over 50 kcal/mol. T h e catalytic effect of water o n t h e mechanism h a s been studied by both methods a n d is found to have an enthalpic barrier similar t o t h e uncatalyzed mechanism a t t h e 3-21G a n d 6-31G* levels. Thermodynamic properties a r e calculated a t elevated temperatures in order t o predict reaction conditions under which evolution of products might b e expected. Kinetic isotope effects a n d tunneling coefficients a r e also calculated and discussed.
The i n t e r m o l e c u l a r concerted dihydrogen t r a n s f e r , as exemplified b y the h y d r o g e n a t i o n of ethylene by ethane in eq 1, is of considerable interest to both theoreticians and experimentalists. H3CCH3 H,C=CH2 H2C=CH2 H3CCH3 (1)
+
The a b initio calculations were carried out at several different levels." Initially geometries were optimized at the 3-21C Ievcl. By using the
+
(1) (a) Miller, C. E. J . Chem. Educ. 1965, 42, 254-259. (b) Hunig, S.; Muller, H. R.; Thier, W. Angew. Cheni. Int. Ed. Engl. 1965. 4. 271-280. (c) Vidyarthi, S. K.; Willis, C.; Back, R. A,; McKitrick, R. M. J . Am. Chem. Soc. The well-known hydrogenation of olefins by diimide,' the hydrogen 1974, 96, 7647-7650. (d) Willis, C.; Back, R. A,; Parsons, J . M.; Purdon, exchange between cis-9,lO-dihydronaphthaleneand various olefins2 J. G. J . Am. Chem. SOC.1977, 99, 4451-4456. (2) Doering, W. V. E.; Rosenthal, J . W. J . Am. Chem. SOC.1967, 89. and the transfer of hydrogen from hydroxymethylene to alkenes3 4534-4535. are examples of this reaction. The reaction in eq 1 has been used (3) Ahmed, S. N.; McKee, M. L.; Shevlin, P. B. J . Am. Chem. SOC.1985, as an e x a m p l e of W o o d w a r d - H o f f m a n symmetry allowed reac107, 1320-1 324. t i o n ~ . ~A q u a n t i t a t i v e t h e o r e t i c a l analysis of this reaction has (4) (a) Woodward, R. B.; Hoffman, R. The Conseraation of Orbital Symmetry; Verlag Chemie: Weinheim, 1971; pp 141-144. (b) Goddard, W. been carried out by Feller, Schmidt, and Ruedenbergs who found A. J . A m . Chem. SOC.1972, 94, 793-807. a barrier of between 69 and 77 kcal/mol which was relatively (5) Feller, D. F.; Schmidt, M. W.; Ruedenberg, K. J . Am. Chem. SOC. insensitive to basis set at the SCF or MCSCF-FORS levels. The 1982, 104, 960-967. symmetric s t r u c t u r e was determined to be a transition structure (6) Limbach, H. H.; Hennig, J.; Gerritzen, D.; Rumpel, H. J . Chem. Soc.. Faraday Trans. 1982, 74, 229-243. at the 3 - 2 1 G level. A t h e o r e t i c a l s t u d y 3 of the reaction of hy(7) Limbach, H . H.; Hennig, J.; Kendrick, R.; Yannoni, C. S. J. Am. droxymethylene with ethylene found t h a t at the 3-21G level b o t h Chem. Soc. 1984, 106, 4059-4060. hydrogens have transferred to approximately the same e x t e n t in ( 8 ) Sarai, A. J . Chem. Phys. 1982, 76, 5554-5563. the t r a n s i t i o n s t r u c t u r e . O t h e r studies6-I2 of coupled hydrogen (9) Gerritzen, D.; Limbach, H. H. J . Am. Chem. SOC.1984, 106, 869-879. (10) Dewar, M. J. S.; Mertz, K. M. J. Mol. Strurt. 1985, 124, 183-185. motion include the free base porphine,&*azophenine,6.I0and acetic (11) Hermes, J . D.; Cleland, W. W. J . Am. Chem. SOC.1984, 106, a ~ i d / m e t h a n o l . ~Most . ~ analogous to the present work is an 7263-7264. e x p e r i m e n t a l study" of t h e o x i d a t i o n of glucose 6 - p h o s p h a t e by (12) (a) Ek, M.; Ahlberg, P. Chenz. Scr. 1980, 16, 62-63. (b) Yamabe, a reactant t h a t accepts a hydride ion and is catalyzed b y an enzyme T.; Yamashita, K.; Kaminoyama, M.; Kuizumi, M.; Tachibana, A,; Fukui, H . J . Phys. Chem. 1984, 88, 1459-1463. which simultaneously accepts a proton. (1 3) Rzepa, H. S.; Miller, J. J . Chem. SOC.Perkin Trans. 2 1985, 7 17-723. Another example of a degenerate dihydrogen exchange is that (14) (a) Dewar, M. J . S.; Thiel, W . J . Am. Cheni. Sor. 1977, 99, b e t w e e n m e t h a n o l a n d f o r m a l d e h y d e (eq 2) which has been 4899-4907. (b) Dewar, M. J. S.; Thiel, W. J . Ani. Chem. SOC.1977, 99, predictedI3 by MNDO t o h a v e a high barrier of 87.2 k c a l / m o l . 4907-4917. (c) Dewar, M. J. S. J . Mol. Struct. 1983, 100, 41-50. (15) (a) Lauer, G.; Schulte, K.-W.; Schweig, A,; Thiel, W . Theor. Chim. H3COH H,C=O -+ H2C=O H,COH (2) Acta (Berlin) 1979, 52, 319-328. (b) Thiel, W. J . Am. Chem. Sor. 1981, 103, 1413-1420. (c) Schroder, S.; Thiel, W. J . Am. Chem. SOC.1985, 107, In t h e present investigation, a d e t a i l e d study of this reaction is 4422-4430. carried out at t h e ab initio as well as the MNDO levels. These (16) (a) Dewar, M . J . S.; Rzepa, H. S. J . Ani. Chem. Soc. 1977, 99, investigations reveal a significant difference between t h e barriers 7432-7439. (b) Dewar, M. J. S.; Ford, G. P.; McKee, M. L.: Rzepa, H . S.; Thiel, W.; Yamaguchi, Y. J . Mol. Struct. 1978, 43, 135-1 38. (c) Dewar, M. calculated by semiempirical and ab initio m e t h o d s . MNDO has J . S.; Fox, M. A.; Campbell, K. A,; Chen, C.-C.; Friedheim, J . E.; Holloway, been used extensively for studies of reaction mechanisms and found M. K.; Kim, S. C.; Liescheski, P. B.; Pakiari, A. M.; Tien, T.-P.; Zoebrisch, to yield reasonable results. The present disagreement in predicted E. G. J . Compur. Chem. 1984, 5, 480-485. (d) Brown, S. B.; Dewar, M. J. barrier heights between the two methods may h a v e implications S.; Ford, G. P.; Nelson, D. J.; Rzepa, H. S. J . Am. Chem. SOC.1978, 100, 7832-7836. (e) Rzepa, H. S.; Dewar, M. J. S. J . Am. Chem. SOC.1978,100, for types of reactions which m a y not be accurately m o d e l l e d by 784-790. (0 Olivella, S.; Urpi, F.; Villarrasa, J. J . Comput. Chem. 1984, 5, the MNDO method. 230-236. DeKock, R. L.; Jasperse, C. P. Inorg. Chem. 1983,22, 3839-3843. (g) For an extensive index to MNDO calculations, see: Clark, T. A HandMethod of Calculation boodk of Computational Chemistry; Wiley: New York, 1985. T h e semiempirical calculations were carried out by using the ( 1 7) References to basis sets used are collected here. The program package M N D O k 4or MNDOCIS programs. The M N D O method has been used GUASSIAN 8 2 was used throughout. Carnegie-Mellon University: Binkley, J. to calculate a number of properties including activation e n e r g i e ~ , ] ~ . ~ ~S.; ~ Frisch, M.; Raghavachari, K.; Fluder, E.; Seeger, R.; Pople, J. A . 3-21G frequencies,16belectronic excited states,16c isotope effects,'6d electron basis: Binkley, J . S.; Pople, J. A.; Hehre, W. J. J . Am. Chem. Sor. 1980, 102, 939. 6-31G basis: Hehre, W. J.; Ditchfield, R.; Pople J . A. J . Chem. Phys. affinities,16' proton affinities,16' and others.I6g MNDOC'5b is a repar1972.56.2257. 6-31G* basis: Hariharan, P. C.; Pople, J . A. Theor. Chim. ameterized version of M N D O which explicitly includes the effects of Acta 1973, 28, 213. Gordon, M. S., Chem. Phys. Lett. 1980, 76, 163. Francl, correlation via the B W E N perturbational approach. Although groundM. M.; Pietro, W . J.; Hehre, W. J.; Binkley, J. S.; Gordon, M . S.; Defrees, state properties are similarly well reproduced, M N D O C seems to do D. J.; Pople, J. A. J . Chem. Phys. 1977, 77, 3654. MP2 correlation treatment: much better than M N D O in predicting activation energies.lSc Mdler, C.; Plesset, M. S. Phys. Rec. 1934, 46, 618. Pople, J. A,; Binkley, J . S.; Seeger, R. I n ? . J . Quantum Chem., Symp. 1976, I O , 1. CPHF: Pople, 'Auburn University. J . A.; Krishnan, R.; Schlegel, H. B.; Binkley, J. S. I n t . J . Quantum Chem., Imperial College of Science and Technology. Sym. 1979, 13, 225. +
+
+
0002-7863/86/l508-5793$01.50/0
0 1986 American Chemical S o c i e t y
5794 J. Am. Chem. SOC.,Vol. 108, No. 19, 1986
McKee et al.
Table 1. Calculated Energies (-hartrees), Zero Point Energies (kcal mol-] at OK), Entropies, and Heat Capacities (cal deg-' mol-] at 298 K, 1 atm) at the M N D O and a b Initio Levels parmtr
H2O
H$=O
TS2"
H3COH
TS,b
AH{ ZPE S
-60.9 14.43 44.93
M N D O geometry -33.0 -57.4 17.99 33.95 52.23 57.02
3-2 1G 6-31G 6-31G* MP2/6-31G ZPE S C"
75.58596 75.98454 76.00977 76.1 1295 13.67 45.09 5.99
3-21G geometryd 113.22182 114.39802 11 3.80827 I 14.98760 113.86529 115.03378 114.02473 1 15.20295 18.18 34.19 52.14 56.64 6.25 8.42
227.55013 228.7 1210 228.8 1046 229.16998 5 1.97 66.40 13.90
303.15232 304.69944 304.80983 305.28980 67.66 78.53 21.39
6-31G* MP2/6-3 1G* ZPE S C.
76.01075 76.19837 14.42 44.99 5.99
6-3 1G* geometry' 113.86633 115.03542 114.17259 115.35217 18.32 34.72 52.10 56.56 6.26 8.34
228.81380 229.47278 51.61 67.03 14.15
304.81434 305.67265 66.10 76.36 20.78
-3.2 49.72 67.09
-41.0 67.81 91.30
OTransition structure for eq 2. bTransition structure for eq 7. CHeats of formation in kcal/mol. dThermodynamic properties (ZPE, S, C,) are calculated at the 3-21G//3-21G level. 'Thermodynamic properties are calculated at the 6-31G*//6-31G1 level.
/A\
\
1.185 (1198) 11.2101
..
156.7 1408.81 l152.21 1110.81 1150.M
Table 11. Thermodynamic Properties" and Isotope Effectsb in Concerted Dihydrogen Transfer Reactions MNDO 11.3Wl
H'
il 3661
AH* AsLs' ~
I1 3981 0102
2.321 (2 326) 12.3361
Figure 1. Structural parameters for the transition structure of eq 2. Values are for the 6-31G* basis, (3-21G), and [ M N D O ] . 3-21G geometries, single point calculations were made at the 6-31G* and MP2/6-3 1 G levels in order to determine relative energies at the additivity levells (Le., [MP2/6-3lG*]//3-2lC). In the next level of approximation, geometries were optimized at the 6-31G* level, and single point calculations were made at the MP2/6-31G* level. Further, frequency calculations were made at the 3-21G and 6-31G* levels in order to determine zero point energylQaand other thermodynamic proper tie^.'^^.^ Table I contains various molecular properties (energies, heat capacities, zero point energies) for species calculated at different levels while Table I1 contains activation parameters calculated a t different levels.
Results and Discussion Ab initio and semiempirical methods agree on the geometry of the C, transition structure (Figure I), predicting that the C-O distances in the transition structure are nearly the same as the average C O distances in formaldehyde and methanol (Table 111). The hydrogen transferring between two oxygens is nearly linear (1 56.7', 6-3 1G*) in contrast to the hydrogen transferring between two carbons which is more bent (138.0', 6-31G*). Comparing the Mulliken charges of the transferring hydrogens in the transition structure to the charges in methanol, one sees a 0.145e decrease (more positive) in the charge of the hydrogen between the two oxygens at the 6-31G* level (0.1 14e; 3-21G) and a 0.188e increase (more negative) in the charge of the hydrogen between the two carbons (0.161e; 3-21G). Clearly the changes in the charges are in the direction of a proton transfer between oxygens and hydride transfer between carbons. One of the most significant results of the present study is the relatively low barrier for this reaction as predicted by a b initio (18) McKee, M. L.; Lipscomb, W. N. J . A m . Chem. SOC.1981, 103, 4673-4676. N o h , R. H.; Bouma, W. J.; Radom, L. Chem. Phys. Lett. 1982, 89, 497-500; McKee, M. L.; Lipscomb, W. N. Inorg. Chem. 1985, 24, 762-764. (19) (a) Hout, R. F.; Beverly, A. L.; Hehre, W. J. J . Compuf,Chem. 1982, 3, 234-250. (b) Cremer, D. J . Compuf. Chem. 1982, 3, 165-177. (c) McQuarrie, D. A. SfafisficalThermodynamics, Harper & Row, New York, 1973.
ACP* KIE(6D) KIE(OD0) KIE(OD0, CH2DCH2) KIE(CHzDCH2) KIE(CD2HCH2)
AH* rls' ACP* KIE(8D)' KIE(2ODO) KIEiCH,DCH,)
[MP2/6-3 l G * ] / / 3-2 I G
MP2/6-3 1 G * / / 6-31G*
Reaction 2' 87.2 38.8 -42.2 -42.1 -2.8 3.31 2.5 2.19 1.7 3.36 2.7 1.48 0.76
31.2 -41.6 -2.4 3.0 2.0 3.2
1.6 0.9
1.6 0.9
Reaction 7 d 110.2 44.8 -62.88 -75.0 -3.3 2.10 3.4 1.06 2.4 I .83 1.5
30.3 -77.3 -3.8 5.0 3.3 1.6
"AH' in kcal mol-' at OK and AS'*, AC* in cal deg-' mol-] a t 298 K, 1 atm. bEvaluated for all the hydrogen case compared to a deuterium substituted case (number and location of deuteriums are given in parentheses) at 700 K. Isotope effects are evaluated at the 321G//3-21G and 6-31G*//6-31G* levels. ' H 3 C O H H,C=O HzC=O H3COH. dH3COH H2C=0 H20 H2C=0 H J O H + H2O. 'For purposes of calculating isotope effects at the 6-31G*//6-31G* level, the smaller imaginary mode of 167i cm-' was treated as a real mode.
+
+
+
-+
-+
Table 111. Comparison of Geometric Parameters (A) in the Reactants and Transition Structure of the Reaction C H z = O t CH3OH CH3OH + CH2=O -+
comoarison
MNDO
3-21G
6-31G*
av C - 0 distance in C H 2 = 0 and H,COH C - 0 distance in transtn structure
1.304
1.324
1.292
1.300
1.306
1.275
methods. The barrier is calculated to be 38.8 kcal/mol at the additivity level with zero point correction ([MP2/6-31G*]//3-21G + ZPC//3-21G) and decreases to 31.2 kcal/mol at the MP2/ 6-31G*//6-31G* + ZPC//6-31G* level. In contrast the MNDO and MNDOC methods drastically overestimate this barrier with values of 87.2 and 84.5 kcal/mol, respectively. Since both the hydrogen transfer from ethane to ethylene in eq 1 and the hydrogenation of formaldehyde by methanol in eq 2 are symmetry allowed (52s ~ 2 +s u2s cycloaddition^,^ the
+
J . A m . Chem. Soc., Vol. 108, No. 19, 1986
Dihydrogen Exchange between Methanol and Formaldehyde
5195
Table IV. Comparison of a b Initio Enthalpic Barrier (kcal/mol) and Geometric Parameters (Distance from Carbon or Oxygen to Transferring Hydrogen) in the Transition Structure with M N D O and M N D O C ~
theimodynamic or eeometric values
-sc&
I
-
i
J-
MNDOC
"best"
Reaction l o 73.5 1.379
62.9 1.366
69.3d
84.5 1.206 I ,388
3 I .2'
C-H
Reaction 2' 87.2 1.210 1.398
AH' 0-H
Reaction 5' 39.0 1.223
38.8 1.233
4.Y
AH' C-H AH'
0-H
/
1
\
/
bcaC-d
I
I
Figure 2. Partial correlation diagram for the formation of the transition structure in the concerted dihydrogen exchange between ethane and ethylene.
reason for the large differences in their activation energies is of interest. In the ethane ethylene reaction, the relevant orbitals are a symmetric and antisymmetric C-H combination and the K orbital. When these orbitals are combined to form the transition structure orbitals for the pericyclic reaction as shown in Figure 2, the H O M O of the activated complex has a node between the two transferring hydrogens leading to antibonding interactions in the transition structure. A discussion of the reasons for the high barrier in the symmetry allowed ethane-ethylene reaction has led to the conclusion that this antibonding interaction is a major f a ~ t o r .The ~ fact that the dihydrogen transfer from diimide to ethylene is facile was ascribed to the thermodynamic driving force associated with the exothermicity of N, formation. While there is no doubt that thermodynamic factors affect the heights of the barriers in these dihydrogen transfers, the results of the present study argue that this cannot be the whole story. Although the hydrogen transfers in eq 1 and 2 are both isoenergetic, the reaction in eq 2 is predicted to proceed with less than half the barrier of that in eq 1. An inspection of the molecular orbitals of the transition structure for the process in eq 2 reveals significant differences from the situation encountered in eq 1. In the former case, the highest occupied orbitals are not those orbitals in the plane of the molecule involving the transferring hydrogens; rather they consist mainly of a symmetric and an antisymmetric combination of the out-of-plane p orbitals on oxygen. These are followed in order of decreasing energy by the in-plane orbitals involving the transferring hydrogens. It is interesting to note that the orbital of b2 symmetry (Figure 3a) in which there is a node on the transferring hydrogen is lower in energy than the a l combination (Figure 3b), a situation exactly opposite to that in the ethylene-ethane reaction. Thus, although this orbital has a node on the transferring hydrogens, it is lower in energy than the analogous orbital in the ethylene-ethane transition structure and exerts a smaller deleterious effect on the barrier. The reason that this three-center bond is favorable in the present case is undoubtedly due to the fact that the electronegative oxygen atoms bear the greatest electron density in the b2 orbital and thus serve to stabilize this orbital. This type of four-electron, three-center bond with electrophilic atoms at the termini has long been thought to be a factor in hydrogen bond formation.20 From this per-
+
(20) (a) Pimentel, G . C. J . Phys. Chem. 1951, 19,446. (b) Pimentel, G . C.; McClellan, A . L. The Hydrogen Bond; W. H. Freeman: San Francisco, 1960; pp 236-238.
MNDO
+
--
+
"Equation 1; CH,=CH, CH,OH C H 3 C H 3 CH,=CH,. CH30H CH,OH CH,=O. 'Equation *Equation 2; C H 2 = 0 5; H C ( O H ) = C H C ( H ) = O O=C(H)CH=CH(OH). d D Z basis MCSCF; ref 5 . 'MP2/6-3lG*//6-31G* + Z P C present work /MP4I6-31C'*//MP2/6-3 IC* ref 26.
+
-+
+
spective, we may view the transition structure as one which has been stabilized by the formation of a hydrogen bond. Although the type of hydrogen bond proposed here differs from the normal hydrogen bond in that both 0-H distances are equal at 1.185 A, the short 0-H bond lengths and the relatively open 0-H-O angle of 156.7' in the transition structure for the process in eq 2 indicate a bonding interaction.2' In contrast, the C-H-C distances of 1.356 8, indicate the antibonding character of this orbital. The importance of the heteroatoms in stabilizing the transition structure for the diimide reduction of ethylene is demonstrated by the fact that the N-H bonds are calculated to be rather short (0.993 A) while long (1.64 A) C-H bonds are predicted.22 In order to investigate why MNDO overestimates the barrier to concerted dihydrogen transfer, the M N D O and MNDOC methods were compared for the reactions in eq 1 and 2. The MNDOC method includes correlation explicitly through the BWEN perturbational methodISbwhile the M N D O method includes correlation through p a r a m e t e r i ~ a t i o n . ' A ~ ~recent comparison has shown that the MNDOC method performs quite well when comparing properties of transition structures (barrier heights, geometries, and zero point energies) with high level ab initio calculation^.'^^ In eq 1 both hydrogens are transferred between carbons while in eq 2 one hydrogen is transferred between carbons and the other between oxygens. Both methods, M N D O and MNDOC, perform similarly for eq 1 and in agreement with a MCSCF-FORS calculation using a DZ basis set.5 For eq 2 M N D O and MNDOC predict very high barriers, which are in disagreement with a b initio predictions (Table IV). Our explanation for the discrepancy involves the basic approximation itself. In MNDO and MNDOC (and M I N D 0 / 3 ) the core-core repulsion for the 0 - H and N-H pairs were estimated by using an arbitarily different empirical function from all other core-core repulsions (eq 3 and 4) but which was found
+ e-C(ARAB+ e-eBRAB) = ZAzB(1 + (RxH/A)e-oxRxH+ e-atlRXH) EAB
E,,
= ZAZB(l
(3) (4)
to improve overall results.14a In most compounds the 0 - H and N-H distances are close to 1 A, and therefore the core-core repulsion integrals are only slightly modified. In the present reaction the much larger 0-H distances yield overestimated core-core repulsion integrals and therefore lead to the calculated higher barriers.23 (21) The three atoms involved in hydrogen bonds tend to have rather open angles: Hamilton, W. C.; Ibers, J. A. Hydrogen Bonding in Solids; W. A . Benjamin: New York, 1968. Olovsson, 1.; Jonsson, P. G . In The Hydrogen Bond, Strucfure and Spectroscopy; Schuster, P.,Zundel, G., Sandorfy, C., Eds.; North Holland: Amsterdam, 1976; Vol. 2 p 401. (22) Pasto, D. J.; Chipman, D. M . J . Am. Chem. SOC.1979, 101, 2290.
5796 J. Am. Chem. SOC.,Vol. 108, No. 19, 1986
McKee et al.
a
b
Figure 3. (a) Jorgensen orbital contour plot (STO-3G//3-21G) for the highest occupied b2 (HOMO-3) in the transition structure of eq 2. (b) Jorgensen orbital contour plot (STO-3G//3-21G) for the highest occupied a , (HOMO-2) in the transition structure of eq 2.
If our explanation is correct, one would expect that the barrier to intramolecular hydrogen migration in malonaldehyde (eq 5 ) would be overestimated by MNDO and MNDOC. An accurate
H
H
ab initio calculation (MP4/6-3 IG**//MP2/6-3 1G*)26predicts a barrier of 4.3 kcal/mol which is in good agreement with an experimentally estimated barrier height of 4.0-5.2 k ~ a l / m o l . ~ ’ In contrast MNDO and MNDOC predict much higher barriers, 39.0 and 38.8 kcal/mol, respectively (Table IV). The transition structure has C, symmetry as shown by one imaginary mode of 2303 cm-l (MNDO). The active hydrogen-oxygen distance of 1.223 A predicted by both MNDO and MNDOC is close to ab initio values of 1.188 and 1.203 A using 6-31G** and MP2/631G** basis sets, respectively. In a recent study28of the reaction between ammonia and formic acid, barriers were calculated at the a b initio and MNDO levels for the step-wise proton transfer reactions in eq 6 as well as for NH3 -t HCOOH
L
H
TS
2 H,N-CH(OH)t TS3
Ls%
NH2CHO
+ H2O
(6)
I
the concerted reaction. The first barrier, (TS,), represents a transfer from nitrogen to a keto oxygen, the second, (TS,), between two oxygens, and the concerted barrier, (TS,), to transfer between nitrogen and a hydroxyl oxygen. MNDO overestimates the three barriers by 19.6,40.7, and 30.8 kcal/mol, respectively, compared to results at the MP4/6-31G**//3-21G level. Other thermodynamic properties however are well reproduced. The authors’ conclusion that “overestimation of the activation energy by MNDO is due mainly to the lack of direct incorporation of correlation effects” may instead be due to the functional form of the 0 - H and N-H core-core repulsion integral. One must conclude that MNDO and MNDOC will not be appropriate for calculating energetics for reactions involving the transfer of a proton (or hydrogen) between oxygens or probably between nitrogens due to an inherent problem in the core-core repulsion functions used between the two pairs of elements. Dewar and co-workers have recently developed a new quantum mechanical molecular model called AM 1 29 which has overcome (23) Attempts have been made to modify the core-core respulsion function for MIND0/324 and MND0.2s (24) Strochbusch, F.; Bratan, S . Z . Narurforsch., A: Phys., Phys. Chem., Kosmophys. 1975, 3OA. 623-626. (25) Burstein, K. Y.; Isaev, A. N . Theor. Chim. Acra (Berlin) 1984, 64, 397-401. (26) (a) Frisch, M. J.; Scheiner, A . C.; Schaefer, H . F.; Binkley, J . S . J . Chem. Phys. 1985, 82, 4194-4198. (b) Carrington, T.; Miller, W. H . J . Chem. Phys. 1986, 84, 4364-4370. (27) Baughaum, S. L.; Smith, Z.; Wilson, E. B.; Duerst, R. W. J . A m . Chem. SOC.1984, 106, 2260. (28) Oie, T.; Loew, G. H.; Burt, S . K.; Binkley, J. S . ; MacElroy, R. D. J . A m . Chem. SOC.1982, 104, 6169-6174.
..- .-,
,
I1 4071 0102
2.818 (2 859)
Figure 4. Structural parameters for the transition structure of eq 7. Values are for the 6-31G* basis, (3-21G basis), and [ M N D O ] .
the failure of MNDO to reproduce hydrogen bonds. The major difference between MNDO and AM1 is the functional form of the core-core repulsion function which in the new formalism is the same for every element pair. The value of the intramolecular hydrogen migration barrier in malonaldehyde by AM1 is reported3* as 22.1 kcal/mol. Catalytic Effect of Water. It is known that water may act as an active participant in some reactions. For example, it is found that a molecule of water reduces the barrier to proton transfer in formamide amidine t a ~ t o m e r i s m . ~ In ’ another example, an extra molecule of water significantly reduces the barrier to hydration of carbon dioxide.32 It was also found33that a pathway exists for the hydration of ketene involving a water dimer via a cyclic transition structure. In contrast to rate enhancements afforded by an “active” water molecule (or dimer), water does not reduce the enthalpic barrier in the concerted dihydrogen exchange between methanol and formaldehyde (eq 7). HlCOH
+ H2C=O + H2O
4
H2C=O
+ H3COH + HZO (7)
Vibrational calculations were performed to confirm the nature of the concerted stationary structure. At all levels one imaginary frequency was found except at the highest level (6-31G*) where a second imaginary frequency (1 67i cm-’) indicated a distortion from C, to a lower C, symmetry. The transition structure34is unusual in that three bonds (two 0 - H and one C-H) are being broken simultaneously. The only other proposed mechanism in (29) (a) Dewar, M. J. S.; Storch, D. M. J . A m . Chem. SOC.1985, 107, 3898-3902. (b) Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P. J . A m . Chem. SOC.1985, 107, 3902-3909. (30) Ford, Dr. G. P., private communication. (31) Zielinski, J. J.; Pokier, R. A,; Peterson, M. R.; Csizmadia, I. G. J . Comput. Chem. 1983, 4, 419-427. (32) Nguyen, M. T.; Ha, T.-K. J . A m . Chem. SOC.1984, 106, 599-602. (33) Nguyen, M. T.; Hegarty, A. F. J . A m . Chem. Sot. 1984, 106, 1552-1 557. (34) Although formally a stationary structure of order two at the 6-31G* level, the designation of transition structure will be used. For purposes of computing zero p i n t energy, entropy, and heat capacity at the 6-31G* level, both negative modes are ignored. However, in the calculation of kinetic isotope effects, the smaller imaginary mode is included as a real mode of the same magnitude (167 cm-I).
J . A m . Chem. SOC.,Vol. 108, No. 19, 1986 5797
Dihydrogen Exchange between Methanol and Formaldehyde
Table V. Calculated Vibrational Frequencies Compared at Various Levles and with Experiment molecule
symmetry of mode
MNDO I960 405 1 4086
frequency (cm-') 3-21G 6-31G* 1800 1827 3814 4070 3947 4188
exotl 1648a 3832 3943
molecule
TS7e
symmetry of mode a" a" a'
frequency (cm-') MNDO 1013i 52 97
3-21'3 20381 126 122
6-31G* 23041 167i 124
152 77 249
162 48 1 395
199 302 33 I
182 278 301
587 469 503
499 521 570
507 283 440
694 587 794
610 64 1 772
8 30 1229 1225
1086 1298 1272
1076 1078 1287
1262 1344 1468
1400 1582 1351
1349 1374 1388
1590 1355 1313
1426 1582
1440
1460 1512 1521
1541 1841 1884
1673 1528 1713
1555 1629 1708
1899 2013 3163
1820 1879 1991
1741 1853 1950
a"
3170 3219 3226
2053 3178 3179
1954 3226 3228
a" a' a'
3651 3704 3831
3270 3273 3959
3324 3326 4129
a'
1215 1210 1491 21 15 3255 3302
1378 1337 1693 1916 3162 3233
1366 1384 1680 2028 3159 323 I
1167' 1249 1500 1746 2783 2843
269 1168 1416
360 1092 1153
348 1I 6 4 1 I88
295' 1033 1060
a' a,,
1235 1438 1504
1254 1480 1638
I289 1508 1638
1165 1345 1455
a"
1417 1565 3228
1686 1698 3177
1652 1664 3185
I477 1477 2844
a'
3198 3390 4007
3217 3294 3868
323 1 3305 4117
2960 3000 368 1
a" a'
26521 158 366
2003i 169 402
2339i 141 320
536 552 69 1
518 637 680
512 643 698
932 799 989
1038 1041 1371
993 1021 1297
1212 1213 1277
1313 1315 1384
1327 1330 1378
1352 1450 1442
1587 1502 1430
1478 1505 1533
1721 1758 1621
1594 1717 1725
1583 1731 I750
1784 1884 3274
1960 I956 3214
1893 1937 3217
3278 3 244 3247
3215 3290 3292
3220 3295 3297
a"
a' a"
a' a'
a//
a' a" a'
a"
a' a' a'
a" a'
a" a" a' a'
exptl
OStrey, G. J . Mol. Spectrosc. 1967, 24, 87. 'Duncan, J. L.; Mallinson, P. D. Chem. Phys. Lett. 1973, 23, 597. 'Shimanouchi, T . Tables of Molecular Vibrational Frequencies Consolidated; National Bureau of Standards: Washington, DC, 1972; Vol. 1. dTransition structure for eq 2. 'Transition structure for eq 7.
this class is the decomposition of glyoxal to hydrogen and carbon monoxide3s where three bonds are also being broken in the transition structure.36 The ab initio transition structures for eq 2 and 7 (Figure 1, Figure 4) are very similar; only a slight modification being necessary to replace H+ with &Of. The OC-H-CO moiety is nearly planar while the two hydrogens of H30+approach from one side. A slightly more lifiear 0-H-0 angle is found (162.9', 6-31G*; 160.7', 3-21G), and the degree of proton transfer between oxygens is nearly the same (OH distances are 1.238 and 1.152 8, at the 6-31G* level; 1.169 and 1.230 8, at the 3-21G level). The oxygens (35) Osamura, Y.;Schaefer, H. F.; Dupuis, M.; Lester, W. A. J . Chem. Phys. 1981,75,5828-5836. (36) However, the triple proton transfer between methanol and acetic acid d i ~ n e r could ~ . ~ be considered in this class.
of methanol and formaldehyde have also "opened up" to accommodate the larger H 3 0 + rather than H+ (2.321 vs. 2.818 A, 6-31G*; 2.326 VS.2.859 A, 3-21G). The MNDO transition structure geometry differs principally in the much shorter forming 0-H bond and the much longer breaking 0-H bond (0.970 and 2.09 A; Figure 4) and a much smaller 0-H-0 angle for hydrogen transfer ( I 18.1', MNDO). The discrepancy in the enthalpic barrier for dihydrogen transfer between M N D O and ab initio actually increases for the water mediated case. The 30 kcal/mol barrier at the ab initio level increases to 110.2 kcal/mol at the M N D O level. Thermodynamic and Kinetic Properties. It is useful to compare thermodynamic and kinetic data at several levels of approximation, The latter may be of particular value to experimental efforts directed toward observing the hydrogenation of formaldehyde by methanol. Since thermodynamic and kinetic properties are de-
5198
J . Am. Chem. SOC.,Vol. 108, No. 19, 1986
McKee et al.
Table VI. Thermodynamic Values" and Rate Constantsb at Different Temperatures for Reaction 2 at the 6-31G*//6-31G* Level T AS* AH* Kc A factord rate constant 300 -41.6 30.5 3.9 x 104 4.8 x 1 0 4 9 30.0 5.1 X l o 4 4.8 X IO-" 500 -42.9 700 900
-43.7 -44.3
29.5 29.0
3.1 1.8
4.3 X l o 4 4.0 X IO4
9.3 7.2
X X
lod
' A H * in kcal mol-' and AS* in cal deg-I mol-'. the following Eyring equation k = K ( k T / h ) ( e s ' I R ) ( e - ~ * / ~CTunneling ~. correction from Bell equation; see text. d A = ( k T / b ) ( e s ' l R ) at 300 and 500 K and A = K ( k T / b ) ( e a S ' / Ra)t 700 and 900 K.
pendent on the calculated vibrational f r e q u e n c i e ~ ,these ' ~ ~ are compared in Table V. In order to predict thermodynamic and kinetic properties at elevated temperatures where reaction may be observed, the enthalpy and entropy of activation must be corrected using eq 8 and 9. The heat capacity at constant volume cuis more easily obtained
AH*^ = A H * O ~ + A C ~ T AA5'*(T-298 K, =
cpIn ( T / 2 9 8 K )
(8) (9)
computationally as the sum of the translational part ( 3 / 2 R )ro, tational part ( 3 / 2 R )and , vibrational part. For an ideal gas, co can be corrected to by using = cc R. In eq 8 and 9 we assume that the heat capacity is constant over the temperature range of interest. The corrected values are given in Table VI. Tunneling is another effect which may be important in the concerted dihydrogen transfer reaction. To approximate a tunneling correction, a simple approximation given by Bell3' for tunneling through a parabolic barrier is used (eq 10).
cp
Qt
cp
+
= j/z~*/sin1 / 2 ~ t
(10)
where kt
= hu,/kT
h = Planck's constant T = absolute temperature ut
= imaginary frequency for the transition structure
When evaluated at temperatures where reaction might occur, the tunneling correction is rather moderate, resulting in approximately a threefold increase in rate at 700 K and a twofold increase a t 900 K (Table VI). Using the thermodynamic properties evaluated at various temperatures, we can predict a rate constant uting the Eyring equation3*(eq 1 1 ) . The last term in eq 11, cAn, is the concen-
tration in the standard state to which the thermodynamic parameters are referred (1 atm, 298 K) raised to one minus the molecularity of the reaction, which lead to the units of atm-' s-I for the rate constant.39 Rate constants given in Table VI are corrected for tunneling only at 700 and 900 K. Taking realistic reaction conditions, we can estimate the rate for the following reaction (eq 12). Under short reaction times the only likely source of undeuterated formaldehyde would be due to the concerted dihydrogen transfer,mechanism. If we assume O=CD2 + H3COH O=CH2 + D2HCOH (12) +
that 0.001 atm of undeuterated product should be easily detectable and starting with 0.1 atm of O=CD2 and 0.9 atm of H3COH at 700 K, then a reaction time of about h is predicted. Experiments to verify this are in progress. Finally, it should be noted that an alternative to the hydrogenation of formaldehyde by methanol is the formation of the hemiacetal in eq 13. Although this reaction is usually acid H,COH H,C=O ---* HOCHZOCH, (13)
+
catalyzed, a recent calculation (4-3 IG//STO-3G) of the activation parameters indicates that this process should be competitive with the hydrogen transfer in eq L 4 0 However, this fact would not hamper efforts to observe the degenerate hydrogen transfer through the use of isotopic labeling as hemiacetal formation should be reversible at high temperatures, and there will always be a steady state of methanol and formaldehyde available for reaction.
Conclusions A postulated mechanism of concerted dihydrogen transfer from methanol to formaldehyde has been carefully analyzed at several levels of theory. We predict an enthalpic barrier of approximately 30 kcal/mol and have set out reaction conditions under which the mechanism might be tested. MNDO and MNDOC overstimate the barrier by about 50 kcal/mol, and it is recommended that these methods not be relied upon for the energetics of proton (or hydrogen) transfer between oxygens or between nitrogens. The catalytic effect of water on the mechanism is small but may be competitive in solution phase. Acknowledgment. M.L.M. and H.S.R. thank Auburn University Computation Center and Imperial College Computer Centre for generous allotments of computer time. Note Added in Proof. Recent experimental atempts4' to detect the concerted exchange mechanism have led instead to large amounts of C O indicating decomposition of the formaldehyde, possibly by a wall reaction. The activation barrier for formation of C O from formaldehyde pyrolysis has been determined42to be 34.4 f 1.3 kcal/mol with a frequency factor of 10'1.8*0.4 Registry No. CH,OH, 67-56-1; H C H O , 50-00-0; H , 1333-74-0; D, 7782-39-0. ~~~~
(39) Robinson, P. J. J . Chem. Educ. 1978, 55, 509-510.
(37) Bell, R. P. The Tunnel Effecf in Chemistry; Chapman and Hall: New York, 1980. (38) Benson, S . W. Thermochemical Kinetics, 2nd ed.;Wiley: New York, 1976.
(40) Williams, I. H.: Spangler, D.;Maggiora, G.M.; Schowen, R. L. J . Am. Chem. SOC.1985, 107, 7717-7723. (41) Cantrell, R., private communication. (42) Chen, C. J.; McKenny, D.J.Can. J . Chem. 1972, 50, 992-998.
